Gwynn died in 2014 at the age of 54 from salivary gland cancer, a disease he attributed to his 31-year habit of chewing smokeless tobacco.
The lawsuit accuses Altria Group Inc. - the multinational tobacco corporation formerly known as Phillip Morris - and several other defendants of manipulating Gwynn into using tobacco when he was a young college star at San Diego State University.
The suit says that the defendants regularly sent Gwynn free samples of smokeless tobacco and misled him about the health risks as part of an effort to market the product to African-Americans, according to The New York Times.
From 1977 to 2008, Gwynn chewed up to two cans of smokeless tobacco per day, using it immediately after waking up and sometimes falling asleep with it between his lip and right cheek, the suit says.
The suit seeks a jury trial and does not specify damages.
"Now that the family understands how he was targeted, they understand that the industry knew they had this highly carcinogenic product and they were marketing it to people like Tony," said David S. Casey, the lead lawyer for the plaintiffs, the Times reported. "They want to hold them accountable and let a jury make a decision as to what is proper in this case."
One of the plaintiffs, Tony Gwynn Jr., said his father never smoked or drank, and that he didn't know the dangers of chewing smokeless tobacco when he first started using the product.
"The tobacco companies were using his addiction to turn him into their ultimate walking billboard," Gwynn Jr. told the Times. "He never knew it, but they were using him to promote their dip to the next generation of kids and fans who idolized him."
Deadspin points out that the suit is strategically timed, as New York and Chicago recently joined the list of Major League Baseball cities to ban tobacco in stadiums.
Gwynn, a 15-time All-Star, was inducted into the Baseball Hall of Fame in 2007. He spent his entire 20-season career with the San Diego Padres.
The Gwynn family will address the media in San Diego on Tuesday at 5 p.m. ET, according to USA Today.